The maximum improvement that can be expected from amplitude and/or phase adaptivity in the performance of an optimum receiver is evaluated in detail for a general class of broad- and narrow-band signals subject to slow Rayleigh fading in the "on-off" mode of operation. The pertinent Bayes risks are evaluated and compared for different states of a priori information. It is found that amplitude adap...
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The problem of computing error probabilities for multi-channel communications using an incoherently terminated receiver is analyzed. The signaling alphabet is composed of two equal-energy, equiprobable, correlated waveforms and the multichannel model is presumed to be of the slowly fading "Rician" type, i.e., each subchannel is presumed to be composed of a fixed or specular component and a scatter...
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Approximations to zero-crossing distributions using the type-B Gram-Charlier series are the concern here. The type-B series consists of a linear function of the Poisson distribution and its derivatives. The probabilityp(n, tau)of exactlynzeros, occurring in a given interval(t, t + tau)of a stationary random process, is expanded in the type-B Gram-Charlier series. T...
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This paper derives a solution to the equationrho (u, s) = N_{0}h(s, u) + int_{0}^{T} rho (t, s)h(t, u) dt, for the case in which the kernel is the covariance function of a stationary random process whose spectral density is a rational function of frequency.
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This paper treats some bandwidth properties of modulated signals of the formq(t) cos [omega_{c}t + varphi(t)]where bothq(t)andvarphi(t)are modulating time functions. For such simultaneous amplitude and angle modulation (AAM), relationships are given connecting the bandwidth of the modulated signal with the properties of the modulating time functions. Some useful bo...
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In various pattern-recognition problems such as classification of photographic data, preprocessing operations result in a two-dimensional array of binary random variables. An optimal recipe for classifying such patterns is described. It combines the use of an orthonormal expansion for the logarithm of probability functions, with the generation of a joint probability distribution from lower-order m...
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Fundamental limitations on the performance of any type of communication system transmitting data from an analog source may be obtained by application of a theorem in Shannon's original paper on information theory. In order to transmit the output of an analog source to a sink with mean-squared error e or less, it is necessary to transmit information from source to sink at rates greater than some mi...
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An upper bound on the minimum distance of a linear convolutional code is given which reduces to the Plotkin bound for the block code case. It is shown that most linear convolutional codes have a minimum distance strictly less than their average distance. A table of the bound for several rates is given for binary codes as well as a comparison with the known optimum values for codes of block length View full abstract»

A new and conceptually simple decoding procedure is developed for all of the cyclic Bose-Chaudhuri-Hocquenghem codes. Iftis the number of errors guaranteed correctable by the Bose-Chaudhuri bound, then any pattern oftor fewer errors can be corrected in a step-by-step manner using this procedure. In the binary case, the method requires only the determination of whether at...
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In prediction problems of communication and control theory, it has become increasingly obvious that there are many applications in which a priori assumptions regarding data statistics are not justified. Thus, systems must be designed to take maximum advantage of whatever statistics are encountered. Unfortunately, these systems are inherently nonlinear in operation, which makes it difficult, ff not...
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Alterations in probability densities produced by iterative application of Bayes' rule are analyzed. Computational requirements for finding a sequence of a posteriori densities remain reasonable despite a growing sample size if and only if a sufficient statistic expressible as a vector of fixed dimension exists. The existence of such a sufficient statistic also insures existence of reproducing a pr...
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One statistical model that has been proposed for the generation of errors in telephone circuits consists of errors with successive inter-arrival times drawn independently from a Pareto distribution, resulting in errors that tend to occur in bursts. These error statistics are applied to a class of burst correcting codes due to Hagelbarger, with particular attention to codes capable of correcting ve...
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The Gorenstein-Zierler decoding algorithm for BCH codes is extended, modified, and analyzed; in particular, we show how to correct erasures as well as errors, exhibit improved procedures for finding error and erasure values, and consider in some detail the implementation of these procedures in a special-purpose computer.
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The solution of Newton's identities over a field of characteristic two is the key step in decoding Bose-Chaudhuri-Hocquenghem codes. This paper introduces a simple transformation of variables which halves the size of the resulting matrix. This transformation can increase the decoder's speed by almost a factor of eight and decrease the decoder's storage requirements by almost a factor of four.
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When the coherence time of a signal propagated through a time-varying medium is less than the signal duration, detection methods using conventional coherent correlation processes are not appropriate. Instead, mixed integration techniques can be used, with the coherent integration interval matched to the signal coherence time. A mixed integration can be simulated quite easily in an optical correlat...
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